跳表（skiplist）的代码实现

跳表（skiplist）是一个非常优秀的数据结构，实现简单，插入、删除、查找的复杂度均为O(logN)。LevelDB的核心数据结构是用跳表实现的，redis的sorted set数据结构也是有跳表实现的。

其结构如下所示：

所有操作均从上向下逐层查找，越上层一次next操作跨度越大。其实现是典型的空间换时间。

具体的细节，可参考维基百科http://en.wikipedia.org/wiki/Skip_list

 

本文作者将redis的sorted set代码进行整理，将跳表部分的实现抽取出来，供参考。

skiplist.h

#ifndef __SKIPLIST_H 2 #define __SKIPLIST_H 3  4 #define SKIPLIST_MAXLEVEL 8  5  6 typedef struct skiplistNode { 7     double score; 8     struct skiplistNode *backward; 9     struct skiplistLevel {10         struct skiplistNode *forward;11     }level[];12 }skiplistNode;13 14 typedef struct skiplist {15     struct skiplistNode *header, *tail;16     unsigned long length;17     int level;18 }skiplist;19 20 #endif

skiplist.c

#include "skiplist.h"  2 #include <stdlib.h>  3 #include <stdio.h>  4   5 skiplistNode *slCreateNode(int level, double score) {  6     skiplistNode * sn = malloc(sizeof(*sn) + level*sizeof(struct skiplistLevel));  7     sn->score = score;  8     return sn;  9 } 10  11 skiplist *slCreate(void) { 12     int j; 13     skiplist *sl; 14  15     sl = malloc(sizeof(*sl)); 16     sl->level = 1; 17     sl->length = 0; 18     sl->header = slCreateNode(SKIPLIST_MAXLEVEL, 0); 19     for(j = 0; j < SKIPLIST_MAXLEVEL; j++) { 20         sl->header->level[j].forward = NULL; 21     } 22     sl->header->backward = NULL; 23     sl->tail = NULL; 24     return sl; 25 } 26  27 void slFreeNode(skiplistNode *sn) { 28     free(sn); 29 } 30  31 void slFree(skiplist *sl) { 32     skiplistNode *node = sl->header->level[0].forward, *next; 33  34     free(sl->header); 35     while(node) { 36         next = node->level[0].forward; 37         slFreeNode(node); 38         node = next; 39     } 40     free(sl); 41 } 42  43 int slRandomLevel(void) { 44     int level = 1; 45     while((rand()&0xFFFF) < (0.5 * 0xFFFF))  46         level += 1; 47     return (level < SKIPLIST_MAXLEVEL) ? level : SKIPLIST_MAXLEVEL; 48 } 49  50 skiplistNode *slInsert(skiplist *sl, double score) { 51     skiplistNode *update[SKIPLIST_MAXLEVEL]; 52     skiplistNode *node; 53  54     node = sl->header; 55     int i, level; 56     for ( i = sl->level-1; i >= 0; i--) { 57         while(node->level[i].forward && node->level[i].forward->score < score) { 58             node = node->level[i].forward; 59         } 60         update[i] = node; 61     } 62     level = slRandomLevel(); 63     if (level > sl->level) { 64         for (i = sl->level; i< level ;i++) { 65             update[i] = sl->header; 66         } 67         sl->level = level; 68     } 69     node = slCreateNode(level, score); 70     for (i = 0; i < level; i++) { 71         node->level[i].forward = update[i]->level[i].forward; 72         update[i]->level[i].forward = node; 73     } 74  75     node->backward = (update[0] == sl->header? NULL : update[0]); 76     if (node->level[0].forward) 77         node->level[0].forward->backward = node; 78     else 79         sl->tail = node; 80     sl->length++; 81     return node; 82 } 83  84 void slDeleteNode(skiplist *sl, skiplistNode *x, skiplistNode **update){ 85     int i; 86     for (i = 0; i < sl->level; i++) { 87         if (update[i]->level[i].forward == x) { 88             update[i]->level[i].forward = x->level[i].forward; 89         } 90     } 91     if (x->level[0].forward) { 92         x->level[0].forward->backward = x->backward; 93     } else { 94         sl->tail = x->backward; 95     } 96     while (sl->level > 1 && sl->header->level[sl->level-1].forward == NULL)  97         sl->level--; 98     sl->length--; 99 }100 101 int slDelete(skiplist *sl, double score) {102     skiplistNode *update[SKIPLIST_MAXLEVEL], *node;103     int i;104 105     node = sl->header;106     for(i = sl->level-1; i >= 0; i--) {107         while (node->level[i].forward && node->level[i].forward->score < score) {108             node = node->level[i].forward;109         }110         update[i] = node;111     }112     node = node->level[0].forward;113     if (node && score == node->score) {114         slDeleteNode(sl, node, update);115         slFreeNode(node);116         return 1;117     } else {118         return 0;119     }120     return 0;121 }122 123 int slSearch(skiplist *sl, double score) {124     skiplistNode *node;125     int i;126 127     node = sl->header;128     for (i = sl->level-1; i >= 0 ;i--) {129         while(node->level[i].forward && node->level[i].forward->score < score) {130             node = node->level[i].forward;131         }132     }133     node = node->level[0].forward;134     if (node && score == node->score) {135         printf("Found %d\n",(int)node->score);136         return 1;137     } else {138         printf("Not found %d\n", (int)score);139         return 0;140     }141 }142 143 void slPrint(skiplist *sl) {144     skiplistNode *node;145     int i;146     for (i = 0; i < SKIPLIST_MAXLEVEL; i++) {147         printf("LEVEL[%d]: ", i);148         node = sl->header->level[i].forward;149         while(node) {150             printf("%d -> ", (int)(node->score));151             node = node->level[i].forward;152         }153         printf("NULL\n");154     }155 }156 157 #ifdef SKIP_LIST_TEST_MAIN158 int main() {159     srand((unsigned)time(0));160     int count = 20, i;161 162     printf("### Function Test ###\n");163 164     printf("=== Init Skip List ===\n");165     skiplist * sl = slCreate();166     for ( i = 0; i < count; i++) {167         slInsert(sl,i);168     }169     printf("=== Print Skip List ===\n");170     slPrint(sl);171 172     printf("=== Search Skip List ===\n");173     for (i = 0; i < count; i++) {174         int value = rand()%(count+10);175         slSearch(sl, value);176     }177     printf("=== Delete Skip List ===\n");178     for (i = 0; i < count+10; i+=2) {179         printf("Delete[%d]: %s\n", i, slDelete(sl, i)?"SUCCESS":"NOT FOUND");180     }181     slPrint(sl);182 183     slFree(sl);184     sl = NULL;185 }186 #endif

测试结果如下所示：

### Function Test ### 2 === Init Skip List === 3 === Print Skip List === 4 LEVEL[0]: 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9 -> 10 -> 11 -> 12 -> 13 -> 14 -> 15 -> 16 -> 17 -> 18 -> 19 -> NULL 5 LEVEL[1]: 0 -> 2 -> 4 -> 7 -> 9 -> 10 -> 11 -> 12 -> 14 -> 15 -> 17 -> 18 -> NULL 6 LEVEL[2]: 7 -> 10 -> 12 -> 14 -> 15 -> NULL 7 LEVEL[3]: 10 -> 14 -> 15 -> NULL 8 LEVEL[4]: 10 -> 14 -> NULL 9 LEVEL[5]: NULL10 LEVEL[6]: NULL11 LEVEL[7]: NULL12 === Search Skip List ===13 Found 114 Found 1815 Not found 2116 Not found 2417 Found 1018 Not found 2019 Found 1420 Found 1021 Found 1922 Found 1823 Not found 2724 Found 525 Found 026 Found 027 Found 1828 Not found 2629 Found 1330 Not found 2831 Not found 2932 Not found 2333 === Delete Skip List ===34 Delete[0]: SUCCESS35 Delete[2]: SUCCESS36 Delete[4]: SUCCESS37 Delete[6]: SUCCESS38 Delete[8]: SUCCESS39 Delete[10]: SUCCESS40 Delete[12]: SUCCESS41 Delete[14]: SUCCESS42 Delete[16]: SUCCESS43 Delete[18]: SUCCESS44 Delete[20]: NOT FOUND45 Delete[22]: NOT FOUND46 Delete[24]: NOT FOUND47 Delete[26]: NOT FOUND48 Delete[28]: NOT FOUND49 LEVEL[0]: 1 -> 3 -> 5 -> 7 -> 9 -> 11 -> 13 -> 15 -> 17 -> 19 -> NULL50 LEVEL[1]: 7 -> 9 -> 11 -> 15 -> 17 -> NULL51 LEVEL[2]: 7 -> 15 -> NULL52 LEVEL[3]: 15 -> NULL53 LEVEL[4]: NULL54 LEVEL[5]: NULL55 LEVEL[6]: NULL56 LEVEL[7]: NULL